Tg³ x+2tg² x+3tgx=0 помогите решить

Question

Tg³ x+2tg² x+3tgx=0 помогите решить

Answer 1

Tg³x + 2tg²x + 3tgx = 0
tgx(tg²x + 2tgx + 3) = 0
tgx = 0                                  tg²x + 2tgx + 3 = 0
x =πn, n ∈ z                         tgx = m
                                             m² + 2m + 3 = 0
                                             D = 2² - 4 * 3 = 4 - 12 = - 8 < 0 - решений нет
Ответ : πn , n ∈ z